Evolutionary graph theory on rugged fitness landscapes

Spatially-resolved datasets are revolutionizing knowledge in molecular biology, yet are under-utilized for questions in evolutionary biology. To gain insight from these large-scale datasets of spatial organization, we need mathematical representations and modeling techniques that can both capture their complexity, but also allow for mathematical tractability. Specifically, it is hard to link previous deme-based or lattice-based models with datasets exhibiting complex patterns of spatial organization and the role of heterogeneous population structure in shaping evolutionary dynamics is still poorly understood. Evolutionary graph theory utilizes the mathematical representation of networks as a proxy for population structure and has started to reshape our understanding of how spatial structure can direct evolutionary dynamics. However, previous results are derived for the case of a single mutation appearing in the population. Complex traits arise from interactions among multiple genes and these interaction can result in rugged fitness landscapes, where evolutionary dynamics can vastly differ from the dynamics of stepwise fixation. Here, we develop a unifying theory of how heterogenous population structure shapes evolutionary dynamics on rugged fitness landscapes. We show that even a simple extension to a two- mutational landscape can exhibit evolutionary dynamics not observed in deme-based models and that cannot be predicted using previous single-mutation results. We also show how to link these models to spatially-resolved datasets and build the networks of the stem cell niches of the bone marrow. We show that these cellular spatial architectures reduce the probability of neoplasm initiation across biologically relevant mutation rate and fitness distributions.